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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Relative Quotes (39 quotes)

Den förslags-mening: att olika element förenade med ett lika antal atomer af ett eller flere andra gemensamma element … och att likheten i krystallformen bestämmes helt och hållet af antalet af atomer, och icke af elementens.
[Mitscherlich Law of Isomerism] The same number of atoms combined in the same way produces the same crystalline form, and the same crystalline form is independent of the chemical nature of the atoms, and is determined only by their number and relative position.
Original Swedish from 'Om Förhållandet emellan chemiska sammansättningen och krystallformen hos Arseniksyrade och Phosphorsyrade Salter', Kungl. Svenska vetenskapsakademiens handlingar (1821), 4. In English as expressed later by James F.W. Johnston, 'Report on the Recent Progress and present State of Chemical Science', to Annual Meeting at Oxford (1832), collected in Report of the First and Second Meetings of the British Association for the Advancement of Science (1833), 422. A Google raw translation of the Swedish is: “The present proposal-sense: that various elements associated with an equal number of atoms of one or several other common elements … and that the similarity in: crystal shape is determined entirely by the number of atoms, and not by the elements.”
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Question: Why do the inhabitants of cold climates eat fat? How would you find experimentally the relative quantities of heat given off when equal weights of sulphur, phosphorus, and carbon are thoroughly burned?
Answer: An inhabitant of cold climates (called Frigid Zoans) eats fat principally because he can't get no lean, also because he wants to rise is temperature. But if equal weights of sulphur phosphorus and carbon are burned in his neighbourhood he will give off eating quite so much. The relative quantities of eat given off will depend upon how much sulphur etc. is burnt and how near it is burned to him. If I knew these facts it would be an easy sum to find the answer.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 183, Question 32. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiassed by personal feeling is characteristic of what may be termed the scientific frame of mind.
From The Grammar of Science (1892), 8.
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Absolute space, of its own nature without reference to anything external, always remains homogenous and immovable. Relative space is any movable measure or dimension of this absolute space; such a measure or dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space, as in the case of space under the earth or in the air or in the heavens, where the dimension is determined from the situation of the space with respect to the earth. Absolute and relative space are the same in species and in magnitude, but they do not always remain the same numerically. For example, if the earth moves, the space of our air, which in a relative sense and with respect to the earth always remains the same, will now be one part of the absolute space into which the air passes, now another part of it, and thus will be changing continually in an absolute sense.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Definitions, Scholium, 408-9.
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Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and external measure (precise or imprecise) of duration by means of motion; such as a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Definitions, Scholium, 408.
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Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.
In Science and Philosophy (1948), 116.
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All interesting issues in natural history are questions of relative frequency, not single examples. Everything happens once amidst the richness of nature. But when an unanticipated phenomenon occurs again and again–finally turning into an expectation–then theories are overturned.
…...
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As an Art, Mathematics has its own standard of beauty and elegance which can vie with the more decorative arts. In this it is diametrically opposed to a Baroque art which relies on a wealth of ornamental additions. Bereft of superfluous addenda, Mathematics may appear, on first acquaintance, austere and severe. But longer contemplation reveals the classic attributes of simplicity relative to its significance and depth of meaning.
In The Skeleton Key of Mathematics (1949), 12.
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Attempts have been made from a study of the changes produced by mutation to obtain the relative order of the bases within various triplets, but my own view is that these are premature until there is more extensive and more reliable data on the composition of the triplets.
In Nobel Lecture (11 Dec 1962). Collected in Nobel Lectures, Physiology or Medicine 1942-1962 (1964).
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Dalton transformed the atomic concept from a philosophical speculation into a scientific theory—framed to explain quantitative observations, suggesting new tests and experiments, and capable of being given quantitative form through the establishment of relative masses of atomic particles.
Development of Concepts of Physics. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 175.
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Geography is … only a branch of statistics, a knowledge of which is necessary to the well-understanding of the history of nations, as well as their situations relative to each other.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5.
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I am willing to believe that my unobtainable sixty seconds within a sponge or a flatworm might not reveal any mental acuity that I would care to ca ll consciousness. But I am also confident ... that vultures and sloths, as close evolutionary relatives with the same basic set of organs, lie on our side of any meaningful (and necessarily fuzzy) border–and that we are therefore not mistaken when we look them in the eye and see a glimmer of emotional and conceptual affinity.
…...
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I have presented the periodic table as a kind of travel guide to an imaginary country, of which the elements are the various regions. This kingdom has a geography: the elements lie in particular juxtaposition to one another, and they are used to produce goods, much as a prairie produces wheat and a lake produces fish. It also has a history. Indeed, it has three kinds of history: the elements were discovered much as the lands of the world were discovered; the kingdom was mapped, just as the world was mapped, and the relative positions of the elements came to take on a great significance; and the elements have their own cosmic history, which can be traced back to the stars.
In The Periodic Kingdom: A Journey Into the Land of the Chemical Elements (1995), Preface, viii.
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In a dispassionate comparison of the relative values of human and robotic spaceflight, the only surviving motivation for continuing human spaceflight is the ideology of adventure. But only a tiny number of Earth’s six billion inhabitants are direct participants. For the rest of us, the adventure is vicarious and akin to that of watching a science fiction movie.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004). [Note: published one year after the loss of seven lives in the Space Shuttle Columbia disaster. —Webmaster]
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It is as true now, as it was in the days when Werner first drew his far-reaching inferences before his charmed listeners, that on the characteristic phenomena and varying distribution of the grand mineral masses of the rock-formations, almost all that concerns the relative habitability of a land depends.
In 'The Relations of Geology', Scottish Geographical Magazine (Aug 1902), 19, No. 8, 409.
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It is hard to hide our genes completely. However devoted someone may be to the privacy of his genotype, others with enough curiosity and knowledge can draw conclusions from the phenotype he presents and from the traits of his relatives.
In The Lives to Come: the Genetic Revolution and Human Possibilities (1997), 127.
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It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is however another advantage, which I think belongs in general to these subjects, that the examinations can be brought to bear on what is really most valuable in these subjects.
In Conflict of Studies and other Essays (1873), 6-7.
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Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional.
(1923). Quoted, without source, in E.T. Bell, Men of Mathematics (1937), Vol. 1, li.
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Men are noisy, narrow-band devices, but their nervous systems have very many parallel and simultaneously active channels. Relative to men, computing machines are very fast and very accurate, but they are constrained to perform only one or a few elementary operations at a time. Men are flexible, capable of “programming themselves contingently” on the basis of newly received information. Computing machines are single-minded, constrained by their “pre-programming.”
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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Neither the absolute nor the relative size of the brain can be used to measure the degree of mental ability in animal or in man. So far as man is concerned, the weights of the brains or the volumes of the cranial cavities of a hundred celebrities of all branches of knowledge all over the world have been listed. … At the bottom of those lists are Gall, the famous phrenologist, Anatole France, the French novelist, and Gambetta, the French statesman, each with about 1,100 cc brain mass. The lists are topped by Dean Jonathan Swift, the English writer, Lord Byron, the English poet, and Turgenev, the Russian novelist, all with about 2,000 cc … Now our mental test! Had Turgenev really twice the mental ability of Anatole France?
In 'The Human Brain in the Light of Its Phylogenetic Development', Scientific Monthly (Aug 1948), 67, No. 2, 104-105. Collected in Sherwood Larned Washburn and ‎Davida Wolffson (eds.), The Shorter Anthropological Papers of Franz Weidenreich Published in the Period 1939-1948: A Memorial Volume (1949), 18.
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No collateral science had profited so much by palæontology as that which teaches the structure and mode of formation of the earth’s crust, with the relative position, time, and order of formation of its constituent stratified and unstratified parts. Geology has left her old hand-maiden mineralogy to rest almost wholly on the broad shoulders of her young and vigorous offspring, the science of organic remains.
In article 'Palæontology' contributed to Encyclopædia Britannica (8th ed., 1859), Vol. 17, 91.
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Objective conscience is the function of a normal being; the representative of God in the essence. Buried so deeply that it remains relatively indestructible.
In On Love & Psychological Exercises: With Some Aphorisms & Other Essays (1998), 52.
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Research may start from definite problems whose importance it recognizes and whose solution is sought more or less directly by all forces. But equally legitimate is the other method of research which only selects the field of its activity and, contrary to the first method, freely reconnoitres in the search for problems which are capable of solution. Different individuals will hold different views as to the relative value of these two methods. If the first method leads to greater penetration it is also easily exposed to the danger of unproductivity. To the second method we owe the acquisition of large and new fields, in which the details of many things remain to be determined and explored by the first method.
In Zum Gedächtniss an Julius Plucker', Göttinger Abhandlungen (1871), 16, Mathematische Classe, 6.
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Success is achievable without public recognition, and the world has many unsung heroes. The teacher who inspires you to pursue your education to your ultimate ability is a success. The parents who taught you the noblest human principles are a success. The coach who shows you the importance of teamwork is a success. The spiritual leader who instills in you spiritual values and faith is a success. The relatives, friends, and neighbors with whom you develop a reciprocal relationship of respect and support - they, too, are successes. The most menial workers can properly consider themselves successful if they perform their best and if the product of their work is of service to humanity.
From 'Getting to the Heart of Success', in Jim Stovall, Success Secrets of Super Achievers: Winning Insights from Those Who Are at the Top (1999), 42-43.
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Suppose that you are in love with a lady on Neptune and that she returns the sentiment. It will be some consolation for the melancholy separation if you can say to yourself at some possibly pre-arranged moment, “She is thinking of me now.” Unfortunately a difficulty has arisen because we have had to abolish Now. There is no absolute Now, but only the various relative Nows, differing according to their reckoning of different observers and covering the whole neutral wedge which at the distance of Neptune is about eight hours thick. She will have to think of you continuously for eight hours on end in order to circumvent the ambiguity “Now.”
In The Nature of the Physical World (1929), 49.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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The importance of a result is largely relative, is judged differently by different men, and changes with the times and circumstances. It has often happened that great importance has been attached to a problem merely on account of the difficulties which it presented; and indeed if for its solution it has been necessary to invent new methods, noteworthy artifices, etc., the science has gained more perhaps through these than through the final result. In general we may call important all investigations relating to things which in themselves are important; all those which have a large degree of generality, or which unite under a single point of view subjects apparently distinct, simplifying and elucidating them; all those which lead to results that promise to be the source of numerous consequences; etc.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 44. In Bulletin American Mathematical Society (1904), 444.
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The key to understanding overpopulation is not population density but the numbers of people in an area relative to its resources and the capacity of the environment to sustain human activities; that is, to the area’s carrying capacity. When is an area overpopulated? When its population can’t be maintained without rapidly depleting nonrenewable resources…. By this standard, the entire planet and virtually every nation is already vastly overpopulated.
In The Population Explosion (1990), 39.
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The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.
…...
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The military engineer had died and his close relative, the civil engineer, had taken his place.
Anonymous
Reported as “one regimental commander declared…” and given as a narrative statement, not within quotation marks. The context is that by World War II, “engineer work in war … covered a far wider technical range than ever before in American military engineering experience,” with increasingly “complex and extensive” operations. In Beck, Bortz, Lynch, Mayo and Weld, 'Introduction' The Corps of Engineers: The War Against Germany (1988), 3. For more background on the change, a footnote cites William Barclay Parsons, The American Engineers in France (1920), 5-7.
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The perfection of the heavenly spheres does not depend upon the order of their relative position as to whether one is higher than another.
As quoted in Edward Grant, Planets, Stars, and Orbs: The Medieval Cosmos, 1200-1687 (1996), 231, citing Oresme, Le Livre du ciel, (1968), Book 2, 507. https://books.google.com/books?isbn=052156509X Edward Grant - 1996
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The significance of a fact is relative to [the general body of scientific] knowledge. To say that a fact is significant in science, is to say that it helps to establish or refute some general law; for science, though it starts from observation of the particular, is not concerned essentially with the particular, but with the general. A fact, in science, is not a mere fact, but an instance. In this the scientist differs from the artist, who, if he deigns to notice facts at all, is likely to notice them in all their particularity.
In The Scientific Outlook (1931, 2009), 38.
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The starting point of Darwin’s theory of evolution is precisely the existence of those differences between individual members of a race or species which morphologists for the most part rightly neglect. The first condition necessary, in order that any process of Natural Selection may begin among a race, or species, is the existence of differences among its members; and the first step in an enquiry into the possible effect of a selective process upon any character of a race must be an estimate of the frequency with which individuals, exhibiting any given degree of abnormality with respect to that, character, occur. The unit, with which such an enquiry must deal, is not an individual but a race, or a statistically representative sample of a race; and the result must take the form of a numerical statement, showing the relative frequency with which the various kinds of individuals composing the race occur.
Biometrika: A Joumal for the Statistical Study of Biological Problems (1901), 1, 1-2.
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This is one of the greatest advantages of modern geometry over the ancient, to be able, through the consideration of positive and negative quantities, to include in a single enunciation the several cases which the same theorem may present by a change in the relative position of the different parts of a figure. Thus in our day the nine principal problems and the numerous particular cases, which form the object of eighty-three theorems in the two books De sectione determinata of Appolonius constitute only one problem which is resolved by a single equation.
In Histoire de la Géométrie, chap. 1, sect. 35.
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Until its results have gone through the painful process of publication, preferably in a refereed journal of high standards, scientific research is just play. Publication is an indispensable part of science. “Publish or perish” is not an indictment of the system of academia; it is a partial prescription for creativity and innovation. Sustained and substantial publication favors creativity. Novelty of conception has a large component of unpredictability. ... One is often a poor judge of the relative value of his own creative efforts. An artist’s ranking of his own works is rarely the same as that of critics or of history. Most scientists have had similar experiences. One’s supply of reprints for a pot-boiler is rapidly exhausted, while a major monograph that is one’s pride and joy goes unnoticed. The strategy of choice is to increase the odds favoring creativity by being productive.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 233-234.
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We cannot rest and sit down lest we rust and decay. Health is maintained only through work. And as it is with all life so it is with science. We are always struggling from the relative to the absolute.
In Max Planck and James Vincent Murphy (trans.), Where is Science Going?, (1932), 200.
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We find that light acquires properties which are relative only to the sides of the ray,–which are the same for the north and south sides of the ray, (using the points of the compass for description’s sake only) and which are different when we go from the north and south to the east or to the west sides of the ray. I shall give the name of poles to these sides of the ray, and shall call polarization the modification which gives to light these properties relative to these poles.
(1811). As quoted in William Whewell, The Philosophy of the Inductive Sciences (1840), 336.
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[As a science hobbyist, hoping to become famous someday, Artie Pinsetter (Lou Costello):] They also laughed at Einstein and his theory of relativity. Now everyone has relatives.
From movie The 30-foot Bride of Candy Rock (1959). Writers, Rowland Barber and Arthur A. Ross. In Larry Langman and Paul Gold, Comedy Quotes from the Movies (2001), 289. This movie, (with its rare appearance of Costello without Bud Abott, his usual comedy partner), was released later in the year of Costello's death.
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[T]he phenomena of animal life correspond to one another, whether we compare their rank as determined by structural complication with the phases of their growth, or with their succession in past geological ages; whether we compare this succession with their relative growth, or all these different relations with each other and with the geographical distribution of animals upon the earth. The same series everywhere!
In Essay on Classification (1851), 196.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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